\psset{unit=1.5,algebraic}
\begin{pspicture*}(-1,-2)(4.5,2.1)
\psaxes[labelFontSize=\scriptstyle,ticksize=-3pt 0,labelsep=2pt]{<->}(0,0)(-0.5,-2)(3.5,2)
\footnotesize
\psplot[linecolor=blue]{0.0001}{3}{ln(x)}
\rput[l](3.1,1.1){$f(x)=\log(x)$}
\uncover<2->{
\psplot[linecolor=red]{0.001}{3}{x-1}
\rput[l](3.1,1.9){$p_{f,1}^1=-1+x$}
}
\uncover<3->{
\psplot[linecolor=green]{0.001}{3}{-1+x-(x-1)^2/2}
\rput[l](2.5,0.5){$p_{f,1}^2=-1+x-\frac{1}{2}(x-1)^2$}
}
\uncover<4->{
\psplot[linecolor=orange]{0.001}{3}{-1+x-(x-1)^2/2+2/6*(x-1)^3}
\rput[r](2.6,1.9){$p_{f,1}^3=-1+x-\frac{1}{2}(x-1)^2+\frac{1}{3}(x-1)^3$}
}
\end{pspicture*}